Hello Students! In this post, you will find the complete NCERT Solutions for Maths Class 12 Exercise 4.5.
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NCERT Solutions for Maths Class 12 Exercise 4.1
NCERT Solutions for Maths Class 12 Exercise 4.2
NCERT Solutions for Maths Class 12 Exercise 4.3
NCERT Solutions for Maths Class 12 Exercise 4.4
NCERT Solutions for Maths Class 12 Exercise 4.5
Examine the consistency of the system of equations in Questions 1 to 6:
Maths Class 12 Ex 4.5 Question 1.
x + 2y = 2
2x + 3y = 3
Solution:
x + 2y = 2,
2x + 3y = 3
Matrix for the above equations is AX = B. 
Hence, the equations are consistent.
Maths Class 12 Ex 4.5 Question 2.
2x – y = 5
x + y = 4
Solution:
2x – y = 5,
x + y = 4
Matrix for the above equations is AX = B. 
Hence, the equations are consistent.
Maths Class 12 Ex 4.5 Question 3.
x + 3y = 5,
2x + 6y = 8
Solution:
x + 3y = 5,
2x + 6y = 8
Matrix for the above equations is AX = B.
Hence, the equations are inconsistent with no solution.
Maths Class 12 Ex 4.5 Question 4.
x + y + z = 1
2x + 3y + 2z = 2
ax + ay + 2az = 4
Solution:
x + y + z = 1
2x + 3y + 2z = 2
ax + ay + 2az = 4
Matrix for the above equations is AX = B.
Hence, the equations are consistent.
Maths Class 12 Ex 4.5 Question 5.
3x – y – 2z = 2
2y – z = – 1
3x – 5y = 3
Solution:
3x – y – 2z = 2
2y – z = – 1
3x – 5y = 3
Matrix for the above equations is AX = B. 
Hence, the equations are inconsistent with no solution.
Maths Class 12 Ex 4.5 Question 6.
5x – y + 4z = 5
2x + 3y + 5z = 2
5x – 2y + 6z = –1
Solution:
5x – y + 4z = 5
2x + 3y + 5z = 2
5x – 2y + 6z = –1
Matrix for the above equations is AX = B.
Hence, the equations are consistent with a unique solution.
Solve system of linear equations, using matrix method, in Questions 7 to 14:
Maths Class 12 Ex 4.5 Question 7.
5x + 2y = 4
7x + 3y = 5
Solution:
The given system of equations can be written as
Maths Class 12 Ex 4.5 Question 8.
2x – y = – 2
3x + 4y = 3
Solution:
The given system of equations can be written as
Maths Class 12 Ex 4.5 Question 9.
4x – 3y = 3
3x – 5y = 7
Solution:
The given system of equations can be written as
Maths Class 12 Ex 4.5 Question 10.
5x + 2y = 3
3x + 2y = 5
Solution:
The given system of equations can be written as
Therefore, x = –1 and y = 4.
Maths Class 12 Ex 4.5 Question 11.
2x + y + z = 1,
x – 2y – z = 3/2
3y – 5z = 9
Solution:
The given system of equations can be written as
Maths Class 12 Ex 4.5 Question 12.
x – y + z = 4
2x + y – 3z = 0
x + y + z = 2
Solution:
The given system of equations can be written as
Therefore, x = 2, y = –1 and z = 1.
Maths Class 12 Ex 4.5 Question 13.
2x + 3y + 3z = 5
x – 2y + z = – 4
3x – y – 2z = 3
Solution:
The given system of equations can be written as:
Therefore, x = 1, y = 2 and z = –1.
Maths Class 12 Ex 4.5 Question 14.
x – y + 2z = 7
3x + 4y – 5z = – 5
2x – y + 3z = 12
Solution:
The given system of equations can be written as
Therefore, x = 2, y = 1 and z = 3.
Maths Class 12 Ex 4.5 Question 15.
If A = 
, find A-1.
Using A-1, solve the following system of linear equations
2x – 3y + 5z = 11,
3x + 2y – 4z = –5,
x + y – 2z = –3
Solution:
Maths Class 12 Ex 4.5 Question 16.
The cost of 4 kg onion, 3 kg wheat and 2 kg rice is ₹ 60. The cost of 2 kg onion, 4 kg wheat and 6 kg rice is ₹ 90. The cost of 6 kg onion, 2 kg wheat and 3 kg rice is ₹ 70. Find the cost of each item per kg by matrix method.
Solution:
Let the cost of 1 kg onion be ₹ x, the cost of 1 kg wheat be ₹ y and the cost of 1 kg rice be ₹ z. According to the given data, we have the following three equations.
4x + 3y + 2z = 60
2x + 4y + 6z = 90
6x + 2y + 3z = 70
Matrix from the above equations is AX = B.
Therefore, x = 5, y = 8 and z = 8.
Hence, the cost of onion, wheat and rice per kg are ₹ 5, ₹ 8 and ₹ 8, respectively.
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